Irregularities of solar cycle and their theoretical...

Irregularities of solar cycle and their

theoretical modeling

Arnab Rai Choudhuri

Department of Physics

Indian Institute of Science

Are there regularities longer than the cycles?

The even-odd or Gnevyshev-Ohl rule (Gnevyshev & Ohl 1948) –

The odd cycle was stronger than previous even cycle for cycles

10 – 21.

Does the Gleissberg

cycle exist?

Difficult to establish or

refute at present!

Waldmeier effect (Waldmeier 1935)

WE1 – Anti-correlation between cycle strength and rise time

WE2 – Correlation between cycle strength and rise rate

(used to predict strength of a cycle)

Dikpati et al. (2008) claimed that

WE1 does not exist in sunspot

area data!

Karak & Choudhuri (2011)

defined rise time as time to grow

in strength from 20% to 80%

From Karak & Choudhuri (2011)

WE2 is a stronger effect.

WE1 is weaker, but seems to exist!

Choudhuri, Chattejee & Jiang 2007

Jiang, Chatterjee & Choudhuri 2007

Correlation between polar field at minimum and next cycle

Are polar faculae good proxies of

polar field?

From Sheeley (1991)

From Jiang, Chatterjee

& Choudhuri (2007)

Hemispheric asymmetry is never very large

• Strengths in two hemispheres (max ~20% in last few

cycles)

•Two hemispheres going out of phase (max ~1 year)

•Durations of cycles in two hemispheres

Goel & Choudhuri

(2009) – Correlation

between asymmetry in

polar faculae at sunspot

minima and aymmetry

in strength of the next

cycle

Various patterns of cycle irregularities

• Gnevyshev-Ohl or even-odd effect

• Waldmeier effect (rise time or rise rate vs. strength of the

cycle)

• Correlation between polar field at the minimum and the

next cycle

• Hemispheric asymmetry not too large

Possibilities of predicting strengths of future cycles

• Polar field at the minimum as a precursor (connected with

various geomagnetic indices)

• Rise rate (after a cycle has begun)

No reliable method for prediction 7-8 years before the

sunspot peak!

Polar field during

the last minimum

has been very weak

Schatten (2005) and

Svalgaard et al.

(2005) predicted a

weak cycle 24

Surprisingly, the first dynamo-

based prediction by Dikpati &

Gilman (2006) is for a very

strong cycle 24!

A fun plot from Pesnell (2008)

Characteristics of Maunder Minimum

Enough observations (Hoyt

& Schatten 1994)

Sokoloff & Nesme-Ribes

1994 – Butterfly diagram,

hemispheric asymmetry

Usoskin, Mursula & Kovaltsov 2000 – Sudden onset, but gradual

recovery

Beer, Tobias & Weiss 1998 – Results from 10Be ice core data,

solar wind magnetic field continued to have cycles during

Maunder minimum

Miyahara et al. 2004 – Similar conclusion from 14C tree ring

data,cycles within Maunder minimum were longer

Less solar activity => weaker B in solar wind => more cosmic

rays => more production of radio-isotopes 10Be and 14C

History of solar activity before telescopic records reconstructed

by Eddy (1977), Stuiver & Braziunas (1989),Voss et al. (1996),

Usoskin, Solanki & Kovaltsov (2007)

From Usoskin, Solanki & Kovaltsov (2007) – 27 grand

minima and 19 grand maxima in the last 11,000 years!

Are grand minima merely extremes of cycle

irregularities?

• Processes which cause cycle irregularities can

push the Sun into grand minima

• Recovery from grand minima requires B

generation processes not involving sunspots

Definitive answer not known!

Our view:

Dynamo generation of magnetic fields

Decay of tilted bipolar

sunspots – Babcock 1961;

Leighton 1969

Twisting by helical

turbulence – Parker

1955; Steenbeck,

Krause & Radler 1966

α–effect – works only if B is not very strong

Early solar dynamo models were mostly based on the

α-effect

Simulations of flux rise in the rise suggested that B at

the bottom of convection zone is 105 G (Choudhuri

1989; D’Silva & Choudhuri 1993; Fan, Fisher &

DeLuca 1993) – α-effect would be suppressed

Flux transport dynamo models are primarily based on

Babcock-Leighton mechanism

Recovery from grand minima must depend again on

the α-effect – spatial distribution or even sign

unknown!

Flux transport dynamo in the Sun (Choudhuri, Schussler &

Dikpati 1995; Durney 1995)

Differential

rotation > toroidal field

generation

Babcock-

Leighton process >

poloidal field

generation

Meridional circulation

carries toroidal field

equatorward & poloidal

field poleward

Basic idea was given by Wang, Sheeley & Nash (1991)

Flux Transport dynamo

(Choudhuri, Schussler & Dikpati 1995)

High diffusivity model Low diffusivity model

(diffusion time ~ 5 yrs) (diffusion time ~ 200 yrs)

IISc group HAO group

(Choudhuri, Nandy, (Dikpati, Charbonneau,

Chatterjee, Jiang, Karak) Gilman, de Toma)

Differences between these models were systematically

studied by Jiang, Chatterjee & Choudhuri (2007) and Yeates,

Nandy & Mckay (2008)

Arguments in favour of high diffusivity model

• Diffusivity of order 1012 cm2/s is what you expect from

mixing length theory ~(1/3)vl (Parker 1979)

• Helps in establishing bipolar parity (Chatterjee, Nandy &

Choudhuri 2004; Hotta & Yokoyama 2010)

• Keeps the hemispheric asymmetry small (Chatterjee &

Choudhuri 2006; Goel & Choudhuri 2009)

• Fluctuations spread all over the convection zone soon,

explaining many aspects of observations (Jiang, Chatterjee

& Choudhuri 2007)

• Behaves properly on introducing fluctuations in

meridional circulation (Karak & Choudhuri 2011)

Possible causes of solar cycle

irregularities

• Effects of nonlinearities

• Fluctuations in poloidal field generation

• Fluctuations in meridional circulation

Nonlinearity due to back-reaction of B on v

α-quenching:

Long history – Stix 1972; Ivanova & Ruzmaikin 1977;

Yoshimura 1978; Schmitt & Schussler 1989

Has a stabilizing effect instead of producing irregularities

Krause & Meinel 1988; Brandenburg et al. 1989 – Nonlinear

stability may detemine the mode of the dynamo

Weiss, Cattaneo & Jones (1984) found chaos in some highly

truncated models with suppression of differential rotation

Charbonneau, St-Jean & Zacharias (2005), Charbonneau,

Beaubien & St-Jean (2007) – The Gnevyshev-Ohl rule may be

due to period doubling just beyond bifurcation point


irregularities




What is the source of fluctuations in poloidal field generation?

Joy’s law: Bipolar sunspots have tilts

increasing with latitude (D’Silva &

Choudhuri 1993)

Their decay produces poloidal field

(Babcock 1961; Leighton 1969)

Randomness due to large scatter in tilt

angles (caused by convective turbulence

– Longcope & Choudhuri 2002)

Mean field equations obtained by averaging over turbulence

and there must be fluctuations around them

First suggested by Choudhuri (1992) and explored by Moss et

al. (1992) and Hoyng (1993)

Applied to flux transport dynamo by Charbonneau & Dikpati

(2000)

Supported by Dasi-Espuig et al. (2010)

Cause of correlation between the polar field at the

minimum and the next cycle (Jiang, Chatterjee &

Choudhuri 2007)

C – Poloidal field produced here by

Babcock-Leighton mechanism

P – Field advected to the pole by

meridional circulation

T – Poloidal field diffuses to

tachocline to produce next cycle

Correlation arises if C -> T diffusion takes 5-10 years (happens

only in high diffusivity model

Prediction of cycle 24 – Dikpati & Gilman (2006) predict a stong

cycle from low diffusivity model and Choudhuri, Chatterjee &

Jiang (2007) predict a weak cycle from high diffusivity model

A theoretical mean field dynamo model would produce

an ‘average’ poloidal field at the end of the cycle.

The actual poloidal field may be stronger or weaker!

• The code Surya is run from one

minimum to the next minumum

in the usual way

• At minimum we change poloidal

field above 0.8R to match the

observed poloidal field

We adopt the following procedure

(Choudhuri, Chatterjee & Jiang 2007)

All calculations are based on our dynamo model (Nandy &

Choudhuri 2002; Chatterjee, Nandy & Choudhuri 2004)

Correlations seen in numerical simulations with random

kicks at the sunspot minima (from Jiang, Chatterjee &

Choudhuri 2007)

High diffusivity

(our model)

Low diffusivity

(Dikpati-Gilman)

Our final results

for the last

few solar

cycles:

(i) Cycles 21-

23 are

modeled

extremely

well.

(ii) Cycle 24 is

predicted to

be a very

weak cycle!

From Choudhuri, Chatterjee & Jiang (2007)

Charboneau, Blais-Laurier & St-Jean (2004) – Low diffusivity

dynamo simulation with fluctuations in α

Intermittencies over several periods – comparable to diffusive

decay time or dynamo memory

Production of grand minima

Choudhuri & Karak (2009) - Modelling of Maunder minimum

with flux transport dynamo

Assumption : Poloidal field drops to 0.0 and 0.4 of its average

value in the two hemispheres

From Choudhuri & Karak (2009)

During recovery poloidal field in solar wind shows

oscillations, even though there are no sunspots

Choudhuri & Karak (2009) also correctly predicted that

we were not entering another grand minimum!!


irregularities




Period of flux transport dynamo ~ inverse of meridional

circulation speed

Decreases at sunspot maxima

(Hathaway & Rightmire 2010)

Due to Lorentz force?

Does not cause irregularities

(Karak & Choudhuri 2011)

We disagree with Nandy, Munoz-

Jaramillo & Martens (2011)

Possible long-term fluctuations in meridional circulation

from inverse of cycle durations (Karak & Choudhuri 2011)

Suppose meridional circulation slows down

Dynamo period increases

(Yeates, Nandy & Mackay 2008)

Diffusion has more

time to act on the fields

Cycles become weaker

Differential rotation

generates more toroidal

flux

Cycles becomes stronger

Applicable for high

diffusivity dynamo

Applicable for low

diffusivity dynamo

Explanation of Waldmeier Effect (Karak & Choudhuri

2011)

WE2 is easy to explain!

But WE1 is reproduced only in high diffusivity model:

weaker meridional circulation causes both longer cycles and

weaker cycles.

Karak (2010) matched only the periods of sunspot cycles by

varying meridional circulation, but very surprisingly strengths of

many cycles also got matched!

Modelling and prediction of actual cycles by using data of polar

fields at minima should work properly only when variations of

meridional circulation has not been large!!!

Karak (2010) found that a sufficiently large decrease in

meridional circulation can cause grand minimum

Periods during grand minimum should be longer!

Various patterns of cycle irregularities

• Gnevyshev-Ohl or even-odd effect (explained as nonlinear

bifurcation)

• Waldmeier effect (caused by fluctuations of meridional

circulation in high diffusivity model)

• Correlation between polar field at the minimum and the

next cycle (caused by fluctuations in poloidal field generation

mechanism in high diffusivity model)

• Hemispheric asymmetry not too large (due to diffusive

coupling between hemispheres)

Conclusions

Grand minima may be caused by



Recovery from grand minima cannot be due to Babcock-

Leighton mechanism!!

Irregularities of solar cycle and their theoretical...

Documents

Transcript of Irregularities of solar cycle and their theoretical...